You should know that at most clubs Schutzhund is an all day event, that unfortunately you probably need a vehicle for and a crate inside that vehicle to keep your dog in while he/she isn't working.
Most clubs track early in the morning, then move on to obedience and protection in the late morning (all depends on how many people are there to track). You'll need to keep your dog contained, not out on a leash, away from the field while you're waiting your turn to go.
Just to put it into perspective, I train with a group of about 10-15 dogs. It takes us about 3-4 hours to get through the obedience and the protection work. A lot of the dogs are owned by the same people so it doesn't help speed things up, but I'm just pointing out how long it can take and what kind of time commitment it is when you're actually at training.
I think the problem most people have with Schutzhund training is that its unlike anything they've done before when it comes to scheduling. You don't just set up a time, show up, do your thing, and leave. You're almost required to stick around and watch the other dogs go, learn from them, ect.
Not saying a club will turn you down, but I'm just pointing out why it would be difficult to do it if your parents at this point aren't 100% behind it as well.